Some Algebraic Properties of Polynomial Rings

Christoph Schwarzweller, and Artur Korniłowicz. "Some Algebraic Properties of Polynomial Rings." Formalized Mathematics 24.3 (2016): 227-237. <http://eudml.org/doc/288088>.

@article{ChristophSchwarzweller2016,
abstract = {In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]/ is isomorphic to the field of polynomials with degree smaller than the one of p.},
author = {Christoph Schwarzweller, Artur Korniłowicz},
journal = {Formalized Mathematics},
keywords = {polynomial; polynomial ring; polynomial GCD},
language = {eng},
number = {3},
pages = {227-237},
title = {Some Algebraic Properties of Polynomial Rings},
url = {http://eudml.org/doc/288088},
volume = {24},
year = {2016},
}

TY - JOUR
AU - Christoph Schwarzweller
AU - Artur Korniłowicz
TI - Some Algebraic Properties of Polynomial Rings
JO - Formalized Mathematics
PY - 2016
VL - 24
IS - 3
SP - 227
EP - 237
AB - In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]/ is isomorphic to the field of polynomials with degree smaller than the one of p.
LA - eng
KW - polynomial; polynomial ring; polynomial GCD
UR - http://eudml.org/doc/288088
ER -